The Astrophysical Journal Letters, 734:L9 (5pp), 2011 June 10 doi:10.1088/2041-8205/734/1/L9Copyright is not claimed for this article. Printed in the U.S.A.

GALAXY ZOO MORPHOLOGY AND PHOTOMETRIC REDSHIFTS IN THE SLOAN DIGITAL SKY SURVEY

M. J. Way1,2,3

1 NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10029, USA2 NASA Ames Research Center, Space Sciences Division, MS 245-6, Moffett Field, CA 94035, USA

3 Department of Astronomy and Space Physics, Uppsala, SwedenReceived 2011 March 25; accepted 2011 April 21; published 2011 May 18

ABSTRACT

It has recently been demonstrated that one can accurately derive galaxy morphology from particular primaryand secondary isophotal shape estimates in the Sloan Digital Sky Survey (SDSS) imaging catalog. This wasaccomplished by applying Machine Learning techniques to the Galaxy Zoo morphology catalog. Using the broadbandpass photometry of the SDSS in combination with precise knowledge of galaxy morphology should helpin estimating more accurate photometric redshifts for galaxies. Using the Galaxy Zoo separation for spirals andellipticals in combination with SDSS photometry we attempt to calculate photometric redshifts. In the best case wefind that the root-mean-square error for luminous red galaxies classified as ellipticals is as low as 0.0118. Giventhese promising results we believe better photometric redshift estimates for all galaxies in the SDSS (∼350 million)will be feasible if researchers can also leverage their derived morphologies via Machine Learning. These initialresults look to be promising for those interested in estimating weak lensing, baryonic acoustic oscillation, and otherfields dependent upon accurate photometric redshifts.

Key words: galaxies: distances and redshifts – methods: statistical

1. INTRODUCTION

It is commonly believed that adding information about themorphology of galaxies may help in the estimation of photo-metric redshifts (Photo-z’s) when using training set methods.Most of this work in recent years has utilized The Sloan DigitalSky Survey (SDSS; York et al. 2000). For example, as discussedin Way et al. (2009, hereafter Paper II), many groups have at-tempted to use a number of derived primary and secondaryisophotal shape estimates in the SDSS imaging catalog to helpin estimating Photo-z’s. Some examples include using the radiuscontaining 50% and/or 90% of the Petrosian (1976) flux in theSDSS r band (denoted as petroR50_r petroR90_r in the SDSScatalog), concentration index (CI = petroR90_r/petroR50_r),surface brightness, axial ratios, and radial profile (e.g., Collister& Lahav 2004; Ball et al. 2004; Vanzella et al. 2004; Wadadekar2005; Kurtz et al. 2007; Wray & Gunn 2008).

More recently, Singal et al. (2011) have attempted touse Galaxy Shape parameters derived from Hubble SpaceTelescope/Advanced Camera for Surveys imaging data usinga principal component approach and then feeding this informa-tion into their neural network code to predict Photo-z’s, but forsamples much deeper than the SDSS. Unfortunately, they findmarginal improvement when using their morphology estimators.

Another promising approach focuses on the reddening andinclination of galaxies. Yip et al. (2011) have attempted toquantify these effects on a galaxy’s spectral energy distribution(SED). The idea is to use this information to correct theoverestimation of Photo-z’s of disk galaxies.

On the other hand, attempts to morphologically classify largenumbers of galaxies in the universe have gained in accuracyover the past 15 years as better/larger training samples fromeye classification have increased. For example, Lahav et al.(1995) were one of the first to use an artificial neural networktrained on 830 galaxies classified by the eyes of six differentprofessional astronomers. In more recent years, Ball et al. (2004)have attempted to classify galaxies by morphological type usinga neural network approach based on a sample of 1399 galaxies

(from the catalog of Nakamura et al. 2003). Cheng et al. (2011)have used a sample of 984 non-star-forming SDSS early-typegalaxies to distinguish between E, S0, and Sa galaxies. In thepast year two new attempts at morphological classification usingMachine Learning techniques on a Galaxy Zoo (Lintott et al.2008, 2011) training sample have been published (Banerji et al.2010; Huertas-Company et al. 2011). The Banerji et al. (2010)results were impressive in that they claim to obtain classificationto better than 90% for three different morphological classes(spiral, elliptical, and point sources/artifacts).

These works are in contrast to previous work like that ofBernardi et al. (2003) who used a classification scheme basedon SDSS spectra. However, this classification certainly missedsome early-type galaxies from their desired sample due to thepresence of star formation.

In this Letter, we will continue our use of Gaussian processregression to calculate Photo-z’s using a variety of inputs. Thismethod has been discussed extensively in two previous papers(Way & Srivastava 2006; Way et al. 2009).

We utilize the SDSS Main Galaxy Sample (MGS; Strausset al. 2002) and the Luminous Red Galaxy Sample (LRG;Eisenstein et al. 2001) from the SDSS Data Release Seven (DR7;Abazajian et al. 2009). We also utilize the Galaxy Zoo 1 surveyresults (GZ1; Lintott et al. 2011). The Galaxy Zoo project4

(Lintott et al. 2008) contains a total of 900,000 SDSS galaxieswith morphological classifications (Lintott et al. 2011).

While this study does not focus exclusively on the LRGsample, it should be noted that if it is possible to improve thePhoto-z estimates for these objects as shown herein it could alsoimprove the estimation of cosmological parameters (e.g., Blake& Bridle 2005; Padmanabhan et al. 2007; Percival et al. 2010;Reid et al. 2010; Zunckel et al. 2011) using the SDSS as wellas upcoming surveys such as BOSS5 (Cuesta-Vazquez et al.2011; Eisenstein et al. 2011), BigBOSS (Schlegel et al. 2009),and possibly Euclid (Sorba & Sawicki 2011), not to mention

4 http://www.galaxyzoo.org5 Baryon Oscillation Spectroscopic Survey.

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LSST6(Ivezic et al. 2008). It could also contribute to morereliable Photo-z errors, as required for weak-lensing surveys(Bernstein & Huterer 2010; Kitching et al. 2011) and baryonicacoustic oscillation measurements, which are also dependentupon accurate Photo-z estimation of LRGs (Roig et al. 2008).

2. DATA

All of the data used herein have been obtained via theSDSS casjobs server.7 In order to obtain results consistentwith Paper II for both the MGS and LRG samples we usethe same photometric quality flags (!BRIGHT and !BLENDEDand !SATURATED) and redshift quality (zConf>0.95 andzWarning = 0) but using the SDSS DR7 instead of earlier SDSSreleases. These data are cross-matched in casjobs with Columns14–16 in Table 2 of Lintott et al. (2011) extracting the galaxiesflagged as “spiral,” “elliptical,” or “uncertain.” The galaxies“flagged as “elliptical” or “spiral” require 80% of the vote inthat category after the debiasing procedure has been applied;all other galaxies are flagged “uncertain” (Lintott et al. 2011).Debiasing is the processes of correcting for small biases in spindirection and color. See Section 3.1 in Lintott et al. (2011) formore details on debiasing.

Note that the GZ1 sample is based upon the MGS, but theMGS contains LRGs as well. This is why we can analyze bothof these samples. However, the actual LRG survey goes fainterthan the MGS and so we do not find LRG galaxies fainter thanthe MGS limit of rpetrosian �17.77. See Strauss et al. (2002)and Eisenstein et al. (2001) for details on the MGS and LRGsamples.

A number of points from both the LRG and MGS were elim-inated because of either bad values (e.g., −9999) or becausethey were considered outliers from the main distribution ofpoints. The former offenders included petroR90_i (13 pointsin the MGS sample, 1 point in the LRG), mE1_i (43 points,5 points), petroR90Err_i (7177 points, 1262 points), and mR-rCcErr_i (22 points, 12 points). The reason for eliminatingbad mE1_i points is that we use it for calculating aE_i fromTable 2 of Banerji et al. (2010). A small number of outliers werealso removed from the MGS sample, but totaled only 27 points.No such outlier points were removed in the LRG sample. Thisleaves us with a total of 437,273 MGS and 68,996 LRG objects.Using the GZ1 classifications in the MGS there are 45,249 el-lipticals, 119,369 spirals, and 272,655 uncertain (∼62%). Forthe LRG sample there are 27,227 ellipticals and 13,495 spiralsleaving 28,274 uncertain (∼41%).

3. DISCUSSION

Using the morphological classifications from the Galaxy Zooproject first data release (Lintott et al. 2011) we attempt to calcu-late Photo-z’s for four different samples and four combinationsof primary and secondary isophotal shape estimates from theSDSS as seen in Table 1. A larger variety of input combina-tions were tried including those in Table 1 of Banerji et al.(2010). However, we only report those found with the lowestroot-mean-square error (rmse) in Table 1 of this Letter.

The results using the Banerji et al. (2010) suggested isophotalshape estimates as well as others tested in Paper II are foundin Figure 1 and Table 1. In Figure 2 we also show plots of thespectroscopic redshift versus the predicted photometric redshift

6 Large Synoptic Survey Telescope.7 http://casjobs.sdss.org

Table 1Results

Dataa Inputsb σrmsec

MGS–ELL ugriz+Q+U 0.01561 0.01532 0.01620· · · ugriz+P50+CI 0.01407 0.01400 0.01475· · · ugriz+P50+CI+Q+U 0.01641 0.01560 0.01801· · · ugriz+B 0.01679 0.01668 0.01683MGS–SP ugriz+Q+U 0.01889 0.01864 0.01913· · · ugriz+P50+CI 0.01938 0.01927 0.01947· · · ugriz+P50+CI+Q+U 0.01751 0.01747 0.01777· · · ugriz+B 0.02092 0.02089 0.02101LRG–ELL ugriz+Q+U 0.01345 0.01291 0.01420· · · ugriz+P50+CI 0.01334 0.01278 0.01426· · · ugriz+P50+CI+Q+U 0.01584 0.01439 0.01693· · · ugriz+B 0.01180 0.01175 0.01184LRG–SP ugriz+Q+U 0.01520 0.01404 0.01910· · · ugriz+P50+CI 0.01514 0.01474 0.01679· · · ugriz+P50+CI+Q+U 0.01957 0.01870 0.02285· · · ugriz+B 0.01737 0.01728 0.01765

Notes.a MGS: Main Galaxy Sample (Strauss et al. 2002); LRG: luminous red galaxies(Eisenstein et al. 2001); SP: classified as spiral by Galaxy Zoo; ELL: classifiedas elliptical by Galaxy Zoo.b u-g-r-i-z: 5 SDSS dereddened magnitudes; P50: Petrosian 50% light radius inSDSS i band; CI: concentration index (P90/P50); Q: Stokes Q value in i band;U: Stokes U value in i band; B: inputs from Table 2 of Banerji et al. (2010): CI,mRrCc_i, aE_i, mCr4_i, and texture_i.c We quote the bootstrapped 50%, 10%, and 90% confidence levels as in Paper IIfor the root-mean-square error (rmse).

for the inputs that predict the lowest rmse for each of the fourdata sets listed in Table 1. These are more impressive thanone might initially guess. In Paper II we showed how addingadditional bandpasses in the ultraviolet via the Galaxy EvolutionExplorer8 (GALEX; Martin et al. 2005) could naively improvePhoto-z estimation. The same was shown when using additionalbandpasses from the infrared from the Two Micron All SkySurvey9 (2MASS; Skrutskie et al. 2006). However, the resultswere biased because neither GALEX or 2MASS reach the samemagnitude or redshift depth as the full SDSS MGS or LRGsamples. It is easier to get lower rmse estimates of Photo-zwhen you have a smaller range of lower redshifts to fit. For theMGS it is clear from the top two panels in Figure 1 that theGalaxy Zoo objects span a similar range of redshifts and r-bandmagnitudes. On the other hand the situation for the luminous redgalaxies is not as straightforward. Looking at the bottom twopanels of Figure 1 the large second bump at a redshift of z ∼0.35 and r ∼ 18 does not exist. The latter is logical because theGalaxy Zoo catalog was drawn from the MGS and hence thereare no galaxies beyond rpetrosian =17.77 (see Petrosian 1976 fordetails on Petrosian magnitudes) according to their selectioncriteria (Strauss et al. 2002).

Our lowest rmse values come from galaxies categorized asellipticals in the Luminous Red Galaxy Sample using the SDSSu-g-r-i-z bandpass filters and the isophotal shape estimates fromTable 2 of Banerji et al. (2010): ci, mRrCc_i, aE_i, mCr4_i,texture_i. These yield an rmse of only 0.01180, which we believeis the lowest calculated to date for such a large sample of galaxiesmeasured in the bandpasses of the SDSS while also retaining afairly large range of redshifts (0 � z � 0.25) and dereddenedmagnitudes (12 � rpetrosian � 17.77).

8 http://www.galex.caltech.edu9 http://www.ipac.caltech.edu/2mass

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0 10000 20000 30000 400000.01

0.012

0.014

0.016

0.018

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0.022GalaxyZoo MGS elliptical galaxies

RM

SE

0 10000 20000 30000 400000.01

0.012

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0 5000 10000 15000 20000 250000.01

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sample size

RM

SE

GalaxyZoo LRG elliptical galaxies

ugriz+Q+Uugriz+P50+CIugriz+P50+CI+Q+Uugriz+B

2000 4000 6000 8000 10000 120000.01

0.012

0.014

0.016

0.018

0.02

0.022GalaxyZoo LRG spiral galaxies

sample size

Figure 1. Plots of root-mean-square error for a given number of galaxies per 50% bootstrap level with representative errors (10% and 90%). Top two panels: MainGalaxy Sample (elliptical and spiral); bottom two panels: luminous red galaxies (elliptical and spiral).

0 0.1 0.2 0.3 0.40

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RMSE=0.014082

MGS elliptical: ugriz+P50+CI

phot

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ric r

edsh

ift

0 0.1 0.2 0.3 0.40

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MGS spiral: ugriz+P50+CI+Q+U

0 0.1 0.2 0.3 0.40

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LRG elliptical: ugriz+B

spectroscopic redshift

phot

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0 0.1 0.2 0.3 0.40

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RMSE=0.014038

LRG spiral: ugriz+Q+U

spectroscopic redshift

Figure 2. Plots of spectroscopic redshift vs. predicted photometric redshift for the input with the lowest rmse for each of the four given data sets shown in Table 1.

Taking a closer look at the kinds of inputs that improve theresults by galaxy type can be interesting. It is clear from Table 1that the Stokes parameters appear to work better for spiral

than elliptical galaxies. The Stokes parameters measure the axisratio and position angle of galaxies as projected on the sky. Indetail they are flux-weighted second moments of a particular

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0 0.1 0.2 0.30

10000

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ies

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SDSS DR7 MGSGalaxy Zoo spiralsGalaxy Zoo ellipticalsGalaxy Zoo unknown

0 0.1 0.2 0.3 0.4 0.50

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12 14 16 18 200

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SDSS DR7 LRGGalaxy Zoo spiralsGalaxy Zoo ellipticalsGalaxy Zoo unknown

Figure 3. Redshift and r-band dereddened model magnitudes for the Main Galaxy Sample (top two panels) and luminous red galaxies (bottom two panels).

isophote:

Mxx ≡⟨x2

r2

⟩, Myy ≡

⟨y2

r2

⟩, Mxy ≡

⟨xy

r2

⟩. (1)

When the isophotes are self-similar ellipses one finds (Stoughtonet al. 2002):

Q ≡ Mxx − Myy = a − b

a + bcos(2φ),

U ≡ Mxy = a − b

a + bsin(2φ). (2)

The semimajor and semiminor axes are a and b while φ is theposition angle. Masters et al. (2010) demonstrates the efficacy ofusing SDSS derived axis ratios in characterizing the inclinationsof spiral galaxies. This is seen in Table 1 where they offer thesecond best set of inputs when determining photometric redshiftfor spirals. Both Stokes Q and U parameters also display a largerrange of values in the spirals than in the ellipticals. The standarddeviations in Stokes Q and U for spirals are 0.1877 and 0.1500while for ellipticals they are 0.0596 and 0.0459. Hence theyclearly offer more room for possible improvement in the formerthan in the latter.

One of the more surprising results is the difference in usingthe B inputs for the MGS versus LRG ellipticals. In the lattercase these inputs give the lowest rmse results, while in the MGSelliptical case they give the worst. This could be due to the factthat the surface brightness of the LRG galaxies are more easilymodeled by the B inputs than the MGS. The MGS ellipticalsmay still have clumps of star formation that can make the surfacebrightness more difficult to model than the more passive LRGellipticals.

When comparing the MGS and LRG spirals, one starkdifference is clear when utilizing the P50 (Petrosian 50% lightradius in SDSS i band) and CI (Concentration Index = P90/

P50) inputs shown in Table 1. In the MGS spiral case theseadditional inputs yield worse fits, whereas they are among themost useful in the LRG spiral case. This may indicate that MGSspirals are more diverse morphologically than LRG spirals. TheP50 and CI inputs are incapable of helping to model the MGSspiral diversity and simply add noise rather than signal to the fits.Masters et al. (2010) point out that red spirals (read LRG type)will “be dominated by inclined dust reddened spirals, and spiralswith large bulges.” Note that this does not mean that LRG bulgedominated spirals are necessarily S0 galaxies (which would addto their diversity both morphologically and spectroscopically).Lintott et al. (2008) and Bamford et al. (2009) have both shownthat contamination of S0s into spirals is only about 3% in thebest case scenario. So again, perhaps P50 and CI can do a betterjob of modeling LRG spirals because they are less diverse thanMGS spirals.

There are several outstanding issues with using this approachfor studies that may utilize large samples of SDSS LRG derivedPhoto-z’s (e.g., baryonic acoustic oscillations). The first is thatthe GZ1 catalog has only been able to classify (∼59%) of theLRG galaxies as spiral or elliptical. This means that 41% ofour sample cannot benefit from morphology knowledge whenestimating Photo-z’s. Second, the LRGs used herein do not goto the same depth (in redshift or magnitude) as the full LRG(r � 19) catalog since the GZ1 is based on the MGS (r � 17.77).Note also that the GZ1 morphology estimates get worse as onereaches the fainter end of the sample (Lintott et al. 2008). Third,the Machine Learning derived morphologies of Banerji et al.(2010) can only classify up to 90% as accurately as their “byeye” GZ1 training set. These constraints will have to be takeninto account for any studies that attempt to utilize morphologyin Photo-z calculations.

The Photo-z code used to generate the results from thisLetter are available on the NASA Ames Dashlink Web

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site https://dashlink.arc.nasa.gov/algorithm/stablegp and is de-scribed in Foster et al. (2009).

Thanks to Jim Gray, Ani Thakar, Maria SanSebastien, andAlex Szalay for their help with the SDSS casjobs server andJeffrey Scargle for reading an early draft. Thanks goes tothe Galaxy Group in the Astronomy Department at UppsalaUniversity in Sweden for their generous hospitality where partof this work was discussed and completed. We acknowledgefunding received from the NASA Applied Information SystemsResearch Program and from the NASA Ames Research CenterDirector’s Discretionary Fund.

This publication has been made possible by the par-ticipation of more than 160,000 volunteers in the GZproject. Their contributions are individually acknowledged athttp://www.galaxyzoo.org/ Volunteers.aspx. Funding for theSDSS has been provided by the Alfred P. Sloan Founda-tion, the Participating Institutions, the National Aeronauticsand Space Administration, the National Science Foundation,the U. S. Department of Energy, the Japanese Monbuka-gakusho, and the Max Planck Society. The SDSS Web site ishttp://www.sdss.org/.

The SDSS is managed by the Astrophysical Research Con-sortium for the Participating Institutions. The Participating In-stitutions are the University of Chicago, Fermilab, the Insti-tute for Advanced Study, the Japan Participation Group, TheJohns Hopkins University, Los Alamos National Laboratory, theMax-Planck-Institute for Astronomy, the Max-Planck-Institutefor Astrophysics, New Mexico State University, University ofPittsburgh, Princeton University, the United States Naval Ob-servatory, and the University of Washington.

This research has made use of NASA’s Astrophysics DataSystem Bibliographic Services.

This research has also utilized the viewpoints (Gazis et al.2010) software package.

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